Diversity of interaction phenomenon, cross-kink wave, and the bright-dark solitons for the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

The (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation has certain advantages in solving engineering problems. In this paper, based on the generalized bilinear form, we successfully derived the diversity of exact solutions under certain constraints by using the symbolic computation Maple. These solutions have interaction wave solitons, cross-kink wave solitons, and bright-dark solitons. To ensure the accuracy of these solutions, we made a special selection of the parameters involved and made a three-dimensional graph, density graph, and contour graph to illustrate the dynamics of the solutions. The resulting solutions can be used for the study of certain phenomena in physics.

On Bi-gram Graph Attributes

We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as unique insights or against other corpus graphs, attributes such as the graph chromatic number and the graph coloring, graph density and graph K-core. We observe a vast domain of tools and algorithms that can be developed on top of the graph representation; creating such a graph proves to be computationally cheap, and much of the heavy lifting is achieved via basic graph calculations. Furthermore, we showcase the different use-cases for the bi-gram graphs and how scalable it proves to be when dealing with large datasets.

Influence of number of individuals and observations per individual on a model of community structure

Social network analysis is increasingly applied to understand animal groups. However, it is rarely feasible to observe every interaction among all individuals in natural populations. Studies have assessed how missing information affects estimates of individual network positions, but less attention has been paid to metrics that characterize overall network structure such as modularity, clustering coefficient, and density. In cases such as groups displaying fission-fusion dynamics, where subgroups break apart and rejoin in changing conformations, missing information may affect estimates of global network structure differently than in groups with distinctly separated communities due to the influence single individuals can have on the connectivity of the network. Using a bat maternity group showing fission-fusion dynamics, we quantify the effect of missing data on global network measures including community detection. In our system, estimating the number of communities was less reliable than detecting community structure. Further, reliably assorting individual bats into communities required fewer individuals and fewer observations per individual than to estimate the number of communities. Specifically, our metrics of global network structure (i.e., graph density, clustering coefficient, Rcom) approached the ‘real’ values with increasing numbers of observations per individual and, as the number of individuals included increased, the variance in these estimates decreased. Similar to previous studies, we recommend that more observations per individual should be prioritized over including more individuals when resources are limited. We recommend caution when making conclusions about animal social networks when a substantial number of individuals or observations are missing, and when possible, suggest subsampling large datasets to observe how estimates are influenced by sampling intensity. Our study serves as an example of the reliability, or lack thereof, of global network measures with missing information, but further work is needed to determine how estimates will vary with different data collection methods, network structures, and sampling periods.

UNION AND INTERSECTION OF CHAOTIC GRAPHS WITH DENSITY VARIATION

The aim of the present study is to discuss the union and intersection operations on chaotic graphs with density variation; the adjacency and incidence matrices representing the chaotic graphs induced from these operations will be introduced when physical characters of chaotic graphs have the same properties. There are several applications that have been utilized on chaotic graphs with density variation. The most practical applications of these kinds of operations on chaotic graphs with density variation are the internet signal speeds and the variation of green color for different parts of the plant. For example, in botany, in some cases, several plants suffer from a lack of chlorophyll in the damaged parts of the plant. In this case, the plant is represented by a chaotic graph, and the proportion of chlorophyll is represented by the density property, then the appropriate process is applied to increase the chlorophyll percentage in the appropriate place, so these operations help us to choose the suitable operator that satisfies our desires and requests. Keywords: adjacency matrix, incidence matrix, chaotic graph, density, union, intersection.

In Search of the Densest Subgraph

In this survey paper, we review various concepts of graph density, as well as associated theorems and algorithms. Our goal is motivated by the fact that, in many applications, it is a key algorithmic task to extract a densest subgraph from an input graph, according to some appropriate definition of graph density. While this problem has been the subject of active research for over half of a century, with many proposed variants and solutions, new results still continuously emerge in the literature. This shows both the importance and the richness of the subject. We also identify some interesting open problems in the field.

An investigation on the evolution of diabetes data in social Q&A logs

This study investigates the evolution of diabetics’ concerns based on the analysis of terms in the Diabetes category logs on the Yahoo! Answers website. Two sets of question-and-answer (Q&A) log data were collected: one from December 2, 2005 to December 1, 2006; the other from April 1, 2013 to March 31, 2014. Network analysis and at-test were performed to analyze the differences in diabetics’ concerns between these two data sets. Community detection and topic evolution were used to reveal detailed changes in diabetics’ concerns in the examined period. Increases in average node degree and graph density imply that the vocabulary size that diabetics use to post questions decreases while the scope of questions has become more focused. The networks of key terms in the Q&A log data of 2005–2006 and 2013–2014 are significantly different according to thet-test analysis of the degree centrality and betweenness centrality. Specifically, there is a shift in diabetics’ focus in that they have become more concerned about daily life and other nonmedical issues, including diet, food, and nutrients. The recent changes and the evolution paths of diabetics’ concerns were visualized using an alluvial diagram. The food- and diet-related terms have become prominent, as deduced from the visualization results.

The Mouse Cortical Interareal Network Reveals Well Defined Connectivity Profiles and an Ultra Dense Cortical Graph

The inter-areal wiring pattern of mouse cerebral cortex was analyzed in relation to an accurate parcellation of cortical areas. Twenty-seven retrograde tracer injections were made in 19 areas of a 41 area (plus 7 sub-area) parcellation of the mouse neo-, parahippocampal and perirhinal cortex. Flat mounts of the cortex and multiple histological markers enabled detailed counts of labeled neurons in individual areas. A weight index was determined for each area-to-area pathway based on the Fraction of Extrinsically Labeled Neurons (FLNe). Data analysis allowed cross species comparison with the macaque. Estimation of FLNe statistical variability based on repeat injections revealed high consistency across individuals and justifies using a single injection per area to characterize connectivity. The observed lognormal distribution of connections to each cortical area spanned 5 orders of magnitude and revealed a distinct connectivity profile for each area, analogous to that observed in macaque. The resulting graph has a density of 97% (i.e. 97% of connections that can exist do exist), considerably higher than the 66% density reported for the macaque. Our results provide more sharply defined connectivity profiles and a markedly higher graph density than shown in a recent probabilistic mouse connectome.

‘Power to the reader’ or ‘degradation of literary taste’? Professional critics and Amazon customers as reviewers of The Inheritance of Loss

The Inheritance of Loss by Kiran Desai (2006) was critically lauded, gaining many positive periodical reviews and winning both the Man Booker Prize and the National Book Critics Circle Award for Fiction. However, it has received mixed reviews from customers of the online retail giant, Amazon: an arguable expression of the challenge that digital consumerism presents to literature’s longstanding claim to autonomy from the market. In order to understand the relationship between the book’s professional and customer reviews, a collection comprising both was constructed. Qualitative analysis of these reviews was followed by the use of thematic coding to compare sub-collections divided by means of publication and by geographical location, with social network graphs being used to represent similarities between reviews and graph density being employed as a measure of overall similarity. No distinctions were found between reviews when grouped according to geographical location. However, the novel’s professionally published reviews were found to be a more homogeneous group than its Amazon customer reviews, and to be more likely to recommend the novel and to praise it for its humour and its narrative, while customer reviews were found to be more likely to criticise it for its characters, and less likely to quote it or to discuss its political themes. It is argued that this is because the book was produced to satisfy the expectations of a ‘literary’ rather than a ‘popular’ audience, where professional book reviewers represent the former almost by definition.